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3 years ago

Explain how negative powers of 10 can be helpful when writing and comparing small numbers

Mathematics

1 answer:

Luba_88 [7]3 years ago

8 0

Answer:

See explanation

Step-by-step explanation:

Powers of 10 is a very useful way of writing down large or small numbers.

Instead of having lots of zeros, you show how many powers of 10 will make that many zeros.

When you work with small numbers, you should use the negative powers of 10. Just remember for negative powers of 10, move the decimal point to the left. For example,

$0.36=3.6\cdot 10^{-1}\ [\text{Move the decimal point one place to the left}]\\ \\0.036=3.6\times 10^{-2}\ [\text{Move the decimal point two places to the left}]\\ \\0.0036=3.6\times 10^{-3}\ [\text{Move the decimal point three places to the left}]\\ \\...$

When comparing small numbers, write these numbers in scientific notation (only one non-xero digit must be before point) and then

if the powers of 10 are the same in compared numbers are the same, just compare the numbers which are multiplied by these powers of 10. For example, $3.6\times 10^{-6}>2.6\times 10{-6},$ because powers are the same (-6) and $3.6>2.6$
if the powers are different, then the smaller is power, the smaller is number (number with the smaller negative power has more places after decimal point). For example, $3.6\times 10^{-6}> 2.6\times 10^{-7},$ because $-6>-7$

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Look at photo for the question and answer choices... NO LINKS OR BLANK ANSWERS

mamaluj [8]

Answer:

B and E

Step-by-step explanation:

6 0

3 years ago

Please explain (will also give brainliest if you put all the steps)

MrMuchimi

Answer:

A = 139.5 cm^2

Step-by-step explanation:

Ok, let's break it down into pieces. First let's find the area of the main rectangle. We know that the area of a rectangle is as follows:

A = L x W

A = 9 x 12

A = 108 cm^2

Now we need to find the area of the two triangles. There are two ways to approach this. If you can visualize that you can flip the first triangle and slide it against the second, it becomes a rectangle. Then you can simply use the same formula as before with modified numbers.

L = 7 (height of the triangle

W = 4.5 (base of the triangle (half of 9))

A (both triangles) = 7 x 4.5

A (both triangles) = 31.5 cm^2

If you can't quite figure out how to visualize that, you can simply treat them as two independent right triangles. The formula for the area of a right triangle is as follows:

A = (1/2)b x h

b = 4.5

h = 7

A (first triangle) = (1/2)4.5 x 7

A (first triangle) = 15.75 cm^2

The area of the second triangle is identical

A (second triangle) = 15.75 cm^2

The area of the two triangles added together is

A (both triangles) = A (first triangle) + A (second triangle)

A (both triangles) = 31.5 cm^2

As you can see we got the same answer both ways. Now we just have to add the area of the two triangles to the area of the rectangle

A = 108 + 31.5

A = 139.5 cm^2

3 0

3 years ago

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Shawn is playing a game with a set of cards. Half of them are blue and the other half are yellow. In the game, the player guesse

kow [346]

Answer:

No, the law of large numbers says that the proportion of yellow cards should approach the true probability after many trials.

Step-by-step explanation:

3 0

3 years ago

in a box of chocolates, 1/5 of the chocolates contain nuts. the rest of the chocolates do not contain nuts. write down the ratio

valina [46]

Answer:

The ratio of the number of chocolates that contain nuts to the number of chocolates = 1:4

Step-by-step explanation:

The parameters given are;

Proportion of the box of chocolates that contain nuts = 1/5

Proportion of the box of chocolates that do not contain nuts = 1 - 1/5 = 4/5

Therefore, we have in a box of chocolates with five chocolates;

The number of chocolates that contain nuts = 1

The number of chocolates that do not contain nuts = 4

Which gives the ratio of the number of chocolates that contain nuts to the number of chocolates as 1:4.

4 0

3 years ago

Can Someone Answer My Final Answers :) I’d appreciate it so much :)

DaniilM [7]

1. Remember that the perimeter is the sum of the lengths of the sides of a figure.To solve this, we are going to use the distance formula: $d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$
where
$(x_{1},y_{1})$ are the coordinates of the first point
$(x_{2},y_{2})$ are the coordinates of the second point
Length of WZ:
We know form our graph that the coordinates of our first point, W, are (1,0) and the coordinates of the second point, Z, are (4,2). Using the distance formula:
$d_{WZ}= \sqrt{(4-1)^2+(2-0)^2}$
$d_{WZ}= \sqrt{(3)^2+(2)^2}$
$d_{WZ}= \sqrt{9+4}$
$d_{WZ}= \sqrt{13}$

We know that all the sides of a rhombus have the same length, so
$d_{YZ}= \sqrt{13}$
$d_{XY}= \sqrt{13}$
$d_{XW}= \sqrt{13}$

Now, we just need to add the four sides to get the perimeter of our rhombus:
$perimeter= \sqrt{13} + \sqrt{13} + \sqrt{13} + \sqrt{13}$
$perimeter=4 \sqrt{13}$
We can conclude that the perimeter of our rhombus is $4 \sqrt{13}$ square units.

2. To solve this, we are going to use the arc length formula: $s=r \alpha$
where
$s$ is the length of the arc.
$r$ is the radius of the circle.
$\alpha$ is the central angle in radians

We know form our problem that the length of arc PQ is $\frac{8}{3} \pi$ inches, so $s=\frac{8}{3} \pi$ , and we can infer from our picture that $r=15$ . Lest replace the values in our formula to find the central angle POQ:
$s=r \alpha$
$\frac{8}{3} \pi=15 \alpha$
$\alpha = \frac{\frac{8}{3} \pi}{15}$
$\alpha = \frac{8}{45} \pi$

Since $\alpha =POQ$ , We can conclude that the measure of the central angle POQ is $\frac{8}{45} \pi$

3. A cross section is the shape you get when you make a cut thought a 3 dimensional figure. A rectangular cross section is a cross section in the shape of a rectangle. To get a rectangular cross section of a particular 3 dimensional figure, you need to cut in an specific way. For example, a rectangular pyramid cut by a plane parallel to its base, will always give us a rectangular cross section.
We can conclude that the draw of our cross section is:

6 0

3 years ago

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